A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle theta. a. Show that the cross-sectional area of the gutter is modeled by the function A(theta) = 100sin theta+ 100sin thetacos theta b. Graph the function Afor 0 ≤ theta≤ pi/2.[Hint: use a graphing calculator or graphing software.] c. Estimate the value of (theta)that yields the largest cross-section area.

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.